You take a random sample of n = 900 observations from a population with a mean of 100 and a standard deviation of 10. What's the largest value of x you would expect to find?
A. 108
B. 101
C. 100
D. 110
To find the largest value of x you would expect to find, we need to consider the concept of standard deviation.
Standard deviation is a measure of how spread out the values in a data set are around the mean. In this case, the population has a mean of 100 and a standard deviation of 10.
Given that we have a random sample of 900 observations, we can use the formula for the margin of error:
Margin of error = (Z-score) * (standard deviation) / √n
The Z-score corresponds to a specific confidence level, indicating how many standard deviations away from the mean we want to consider. For a commonly used 95% confidence level, the Z-score is approximately 1.96.
Substituting the values into the formula:
Margin of error = 1.96 * 10 / √900
Calculating this, we get:
Margin of error = 1.96 * 10 / 30 = 0.6533 (rounded to four decimal places)
Since we want to find the largest value of x you would expect to find, we need to add the margin of error to the mean:
Largest value of x = mean + margin of error = 100 + 0.6533 = 100.6533
The closest answer choice to 100.6533 is 101, so the correct answer is B. 101.